Question: Ishaan is 2 times as old as William. Twenty years ago, Ishaan was 7 times as old as William. How old is Ishaan now?
Solution: We can use the given information to write down two equations that describe the ages of Ishaan and William. Let Ishaan's current age be $i$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $i = 2w$ Twenty years ago, Ishaan was $i - 20$ years old, and William was $w - 20$ years old. The information in the second sentence can be expressed in the following equation: $i - 20 = 7(w - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = i / 2$ . Substituting this into our second equation, we get: $i - 20 = 7($ $(i / 2)$ $- 20)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 20 = \dfrac{7}{2} i - 140$ Solving for $i$ , we get: $\dfrac{5}{2} i = 120$ $i = \dfrac{2}{5} \cdot 120 = 48$.